Cognitive Psychology Lecture 7: Reasoning October 08 John Toner.

Cognitive Psychology

Lecture 7: Reasoning

October 08

John Toner

Reasoning

Studying the human memory system involves questions about how we acquire and retain knowledge

Problem Solving and Reasoning research investigates what we do with this knowledge

Reasoning involves using knowledge within systems of formal logic

Reasoning

Reasoning can be defined as the mental processes by which people derive conclusions from a given set of premises.

E.g. Thursday is the day after Wednesday - premise

Today is Wednesday - premise

Tomorrow will be Thursday - conclusion

Reasoning

There are two types of reasoning:

Inductive Reasoning: Involves deciding what is probably the case based on one’s knowledge

E.g. Every morning in the past the sun has risen in the east

Therefore the sun will rise in the east tomorrow

ReasoningThere are two types of reasoning:

Inductive Reasoning: Involves deciding what is probably the case based on one’s knowledge

E.g. of a turkey’s inductive reasoningI have been fed every day up to today (23rd Dec)

Therefore I will be fed tomorrow (24th Dec)

Reasoning

Inductive Reasoning:

As this example illustrates, in inductive reasoning, when the premises are true, the conclusion is not necessarily true. The conclusion can only be judged true with a certain degree of probability.

Reasoning

Deductive Reasoning involves conclusions that follow with certainty from the premises.

E.g.

If it is raining in Dublin there will be ripples in the Liffey

It is raining in Dublin

Therefore there are ripples in the Liffey

Inductive Reasoning

We use inductive reasoning all the time to make decisions about the world

It is getting cloudy and dark, its probably going to rain

If I flick the light switch, the light will come on

If I don’t eat something I’ll get hungry

Inductive ReasoningInductive reasoning results in a hypothesisTesting a hypothesis will result in either

confirmation or falsification

• Confirmation involves finding evidence is support of the hypothesis.

• Falsification involves finding evidence that does not support the conclusions.

• NB: A hypothesis cannot be proved

Inductive ReasoningConfirmation Bias:

People tend to test hypotheses by seeking confirming evidence rather than by attempting falsification of the hypothesis.

Confirmation bias is observed for both ordinary people and professional scientists (Tweney, 1998) even though falsification can be regarded as what distinguishes science from unscientific activities (Popper, 1968)

Inductive ReasoningConfirmation Bias:

“The Earth is flat”

Confirmation bias leads to the following test:It appears flat

Falsification leads to the following test:If one sails westward for long enough they will arrive back home from the east

Inductive ReasoningConfirmation bias is evident in peoples social thinking

Stereotyping: “All skinheads are violent”

People are very good at remembering instances that support these judgements

People tend to neglect instances which do not support these judgements

The 2-4-6 taskWason (1960) investigated strategies used by people when

testing hypotheses

Participants were told that there was a general rule for grouping 3 numbers

As an example they were told that ‘2-4-6’ conforms to the rule

They had to suggest examples in order to discover what the rule might be

The 2-4-6 taskThe actual rule was: Three numbers ascending in value

Therefore the following would all conform

4-6-81-3-7100-150-200

People were generally bad at discovering the rule. 28% failed to discover it at any stage

The 2-4-6 taskWhat was happening?

People were coming up with a hypothesis:“The rule is ascending in twos”

They tended to come up with suggestions that confirmed this rule.

“What about 5-7-9. What about 20-22-24”

The problem was that these all conformed so they believed their hypothesis to be true

The 2-4-6 taskIn fact, the best was to test a hypothesis is to try to falsify it

“What about 6-8-9”

Doing this leads to discovery of the rule

The 2-4-6 taskKlayman & Ha (1987) argue that this experiment is flawed if

we try to generalise the findings to real life reasoning

They argue that the difficulty with the 2-4-6 task is that it possesses the unusual characteristic that the correct rule is much more general than any of the initial hypotheses that participants are likely to form.

As a result, positive testing cannot lead to discovery of the correct rule, and negative testing is required

The 2-4-6 taskTweney (1980) carried out tests on a variation of the 2-4-6

task. They were instructed to find two rules rather than just one

One rule called DAX, was “three ascending numbers” (i.e. Wason’s original rule)

The other rule, called MED, was any other triple (i.e. does not obey the DAX rule).

Each time a triplet of numbers was suggested by participants, they were told that it was either a DAX or a MED triplet

The 2-4-6 taskTweney (1980)

People were much better at discovering the DAX rule than in Wason’s original study.

Tweney did not come up with an explanation of the effect

Nevertheless, it shows how the way a task is presented effects how it is tackled, and thus must reveal something about how are reasoning works

The 2-4-6 task• One explanation (proposed by Evans, 1989) is that people

have a positivity bias in their hypothesis testing strategy.

• The idea of positivity bias supposes that people are more likely to make positive tests of their hypothesis than negative tests.

• Since negative testing is required to find the rule in the original 2-4-6 task, participants’ positivity bias makes this task difficult.

• However, the dual goal paradigm allows participants to use positive tests of their hypotheses about the MED rule in order to gather information about the DAX rule.

Deductive ReasoningDeductive reasoning allows us to draw conclusions that are

definitely valid provided that the other statements are assumed to be true

Conditional Reasoning:

If it is raining in Dublin then there are ripples in the Liffey

Deductive ReasoningDeductive reasoning allows us to draw conclusions that are

definitely valid provided that the other statements are assumed to be true

Syllogistic reasoning

Peter Paul Paul Patrick

Deductive ReasoningConditional Reasoning involves deciding something based

on knowledge about something else

Reasoning based on if and then

If it is raining in Dublin there will be ripples in the Liffey

It is raining in Dublin

Therefore there are ripples in the Liffey

Deductive ReasoningConditional Reasoning

It is raining in Dublin (We will call this A)

There are ripples in the Liffey (We call this B)

We know if A, then B

This rule of inference is known as modus ponens


It is raining in Dublin (We will call this A)There are ripples in the Liffey (We call this B)

We also know

If B is false, then A is false

If there are no ripples in the Liffey then it is not raining

This rule of inference is known as modus tollens




What about

If A is false, then is B false?

Not Necessarily!

If it is not raining, there could still be ripples in the Liffey

This is known as denial of the antecedent




What about

If B is true, then is A true?

Not Necessarily!

If there are ripples in the Liffey, then it is not necessarily raining

This is known as affirmation of the consequent

Deductive ReasoningMarcus & Rips (1979) The percentage of subjects endorsing

the various conditional inferences

Deductive ReasoningSyllogistic Reasoning:

Mayo is in Ireland

Ireland is in Europe

Therefore Mayo is in Europe

Deductive ReasoningMistakes with Syllogistic Reasoning:

Biases: People accept believable conclusions and reject unbelievable conclusions irrespective of their logical validity

All French people drink wine

Some wine drinkers enjoy cheese

Therefore some French people enjoy cheese

This conclusion does not follow from the premises

Deductive Reasoning TheoriesThere are three major theories to be considered

• Abstract Rule Theory

• Mental Model Approach

• Probabilistic Approach

Deductive ReasoningAbstract Rule Theories

According to Braine, and others, in several publications, the following processes occur when someone encounters a deductive reasoning problem


1) The premises are comprehended and encoded into a mental representation in working memory

2) Abstract-rule schema’s are applied to these premises in order to derive a conclusion (e.g. modus ponens)

3) Feeder schemas are applied to produce intermediate conclusions

4) Incompatibility rules examine the contents of working memory for any incompatible references (e.g. inferring both ‘A’ and ‘not A’)


1) The premises are comprehended and encoded into a mental representation in working memory

Ireland are playing in a football match. Crowd in pub are watching

2) Abstract-rule schema’s are applied to these premises in order to derive a conclusion (e.g. modus ponens)

If Ireland do well the people watching will be happy. Loud cheer!

3) Feeder schemas are applied to produce intermediate conclusions

I hear a loud cheer during the match

4) Incompatibility rules examine the contents of working memory for any incompatible references (e.g. inferring both ‘A’ and ‘not A’)

Could there be Cyprus fans in the pub? Would the be that loud? Could Ireland fans cheer a Cyprus goal because they want the manager to get sacked?


Braine (1984) argued the reasons why people make errors in reasoning:

1) Comprehension errors: The premises are interpreted incorrectly. (e.g. If there are ripples in the Liffey then it must be raining)

2) Heuristic inadequacy: The participants reasoning processes fail to locate the correct line of reasoning. (They fail to see the link between rain and ripples)

3) Processing errors: The participant fails to attend fully to the task at hand or suffers from memory overload. (Distraction, interruption, not thinking things through)


General assumption:

Normally people reason correctly provided they don’t misunderstand the premises, get distracted etc.


Reasoning error: Affirmation of the consequent

“There are ripples in the Liffey” leads incorrectly to the conclusion “It is raining”

According to Braine et al. (1984) this occurs because of a conversion error

“If it rains there are ripples in the Liffey”

Is replaced by

“If there are ripples in the Liffey, it is raining”


Braine goes on to say that there is an assumption amongst people that we are being given certain information for a reason.

“If you mow the lawn, I will give you 5 euro”

Invites the inference

“If you don’t mow the lawn, I wont give you 5 euro”

How is this exploited in advertising?


Braine et al. reduced the likelihood of a conversion error by providing an additional, clarifying premise:

e.g. If it is raining, then Alicia gets wet

If it is snowing, then Alicia gets wet

Alicia gets wet

Conclusion…


Limitations:

‘Comprehension’ component is under specified, so it is hard to make predictions about how well a person will reason

The theory has only been applied to a limited range of reasoning tasks

Individual differences are de-emphasised.

There is little convincing evidence that people use mental logic when presented with deductive reasoning problems

Deductive ReasoningMental Models

Proposed by Johnson-Laird (1983, 1999)

A mental model is a possibility for the way things are in the world

E.g. Premises

The lamp is on the right of the pad

The book is on the left of the pad

The clock is in front of the book

The vase is in front of the lamp

Conclusion: The clock is to the left of the vase


Here’s this particular model:

book pad lamp

clock vase

We can construct a model that is consistent with the premises and the conclusion. This indicates that the conclusion is valid


Assumptions:

• A mental model describing the given situation is constructed, and the conclusions following from this are generated

• An attempt is made to construct alternative models that will falsify the conclusion

• If a satisfactory alternative model is not found, the conclusion is assumed to be valid

• The construction of mental models taxes the Working Memory system


Assumptions: …continued

• In order to save Working Memory resources people tend to construct models that represent explicitly what is true and not what is false. (Model based on “If it rains there will be ripples in the Liffey”, not on “If there are no ripples in the Liffey, it is not raining”. This is the Principle of truth.

• Problems requiring the construction of mental models are harder to solve that those requiring only one mental model, because of the demands on Working Memory


Johnson-Laird (1983) had participants arrive at a conclusion based on premises

When only 1 model was required 78% drew valid conclusion

When 2 models were required, 29% drew valid conclusion

When 3 models were required 13% drew valid conclusion


Laird & Goldvarg (1997) showed that participants over-emphasis on the principal of truth led to 99% of participants making the wrong conclusion in a hand of cards task

Only one of the following premises is true about a particular hand of cards

(1) There is a king in the hand or there is an ace, or both

(2) There is a queen in the hand or there is an ace, or both

(3) There is a jack in the hand or there is a 10, or both

Is it possible that there is an ace in the hand?


Mental model theory accounts for a wide range of problems and most of its predictions have been confirmed experimentally

Mental models do not require the existence of ‘mental logic’, but rather the theory requires nothing more than the normal processes of comprehension

This leads to the argument that the tests used in reasoning experiments can be used to draw conclusions on everyday real life reasoning


Limitations:

More detail needed as to how mental models are formed and which knowledge we bring forth and use

Ford (1995) Identified spatial and verbal reasoners.

“Neither…could be said to provide evidence of developing mental models that are structural analogues of the world”

Reading

Eyesenck & Keane Chapters 15 & 16

Sternberg Chapter 12

Article:

Schrovens, W. & Schaeken, W. (2003) A critique of Oaksford, Chater, and Larkin's (2000) conditional probability model of conditional reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition. Vol 29(1), pp. 140-149

Animal Ethics APA

http://www.apa.org/science/animal2.html

Cognitive Psychology Lecture 7: Reasoning October 08 John Toner.

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Transcript of Cognitive Psychology Lecture 7: Reasoning October 08 John Toner.